Content deleted Content added
Citation bot (talk | contribs) Alter: template type. Add: bibcode, s2cid, authors 1-1. Removed parameters. Some additions/deletions were parameter name changes. | Use this bot. Report bugs. | Suggested by AManWithNoPlan | #UCB_webform 594/1776 |
Added an important application |
||
Line 23:
Other continuous problems for which quantum algorithms have been studied include finding matrix [[Eigenvalues and eigenvectors|eigenvalues]],<ref>{{Cite journal|last1=Jaksch|first1=Peter|last2=Papageorgiou|first2=Anargyros|date=2003-12-19|title=Eigenvector Approximation Leading to Exponential Speedup of Quantum Eigenvalue Calculation|journal=Physical Review Letters|volume=91|issue=25|pages=257902|arxiv=quant-ph/0308016|doi=10.1103/PhysRevLett.91.257902|pmid=14754158|bibcode=2003PhRvL..91y7902J|s2cid=1855075}}</ref> phase estimation,<ref>{{Cite journal|last=Bessen|first=Arvid J.|date=2005-04-08|title=Lower bound for quantum phase estimation|journal=Physical Review A|volume=71|issue=4|pages=042313|arxiv=quant-ph/0412008|doi=10.1103/PhysRevA.71.042313|bibcode=2005PhRvA..71d2313B|s2cid=118887469}}</ref> the Sturm–Liouville eigenvalue problem,<ref>{{Cite journal|last1=Papageorgiou|first1=A.|last2=Woźniakowski|first2=H|title=Classical and Quantum Complexity of the Sturm–Liouville Eigenvalue Problem|journal=Quantum Information Processing|language=en|volume=4|issue=2|pages=87–127|arxiv=quant-ph/0502054|doi=10.1007/s11128-005-4481-x|year=2005|bibcode=2005quant.ph..2054P|s2cid=11089349}}<br/>{{Cite journal|last1=Papageorgiou|first1=A.|last2=Woźniakowski|first2=H.|date=2007-04-01|title=The Sturm-Liouville Eigenvalue Problem and NP-Complete Problems in the Quantum Setting with Queries|journal=Quantum Information Processing|language=en|volume=6|issue=2|pages=101–120|arxiv=quant-ph/0504191|doi=10.1007/s11128-006-0043-0|s2cid=7604869|issn=1570-0755}}</ref> solving [[differential equation]]s with the [[Feynman–Kac formula]],<ref>{{cite arXiv|last=Kwas|first=Marek|date=2004-10-18|title=Complexity of multivariate Feynman-Kac path integration in randomized and quantum settings|eprint=quant-ph/0410134}}</ref> initial value problems,<ref>{{Cite journal|last=Kacewicz|first=Bolesław|title=Randomized and quantum algorithms yield a speed-up for initial-value problems|journal=Journal of Complexity|language=en|volume=20|issue=6|pages=821–834|doi=10.1016/j.jco.2004.05.002|year=2004|arxiv=quant-ph/0311148|s2cid=9949704}}<br/>{{cite arXiv|last=Szczesny|first=Marek|date=2006-12-12|title=Randomized and Quantum Solution of Initial-Value Problems for Ordinary Differential Equations of Order k|eprint=quant-ph/0612085}}<br/>{{Cite journal|last=Kacewicz|first=Bolesław|title=Improved bounds on the randomized and quantum complexity of initial-value problems|journal=Journal of Complexity|language=en|volume=21|issue=5|pages=740–756|doi=10.1016/j.jco.2005.05.003|year=2005|arxiv=quant-ph/0405018|s2cid=5934254}}</ref> function approximation<ref>{{Cite journal|last1=Novak|first1=Erich|last2=Sloan|first2=Ian H.|last3=Woźniakowski|first3=Henryk|date=2004-04-01|title=Tractability of Approximation for Weighted Korobov Spaces on Classical and Quantum Computers|journal=Foundations of Computational Mathematics|language=en|volume=4|issue=2|pages=121–156|arxiv=quant-ph/0206023|doi=10.1007/s10208-002-0074-6|s2cid=10519614|issn=1615-3375}}<br>
{{Cite journal|last=Heinrich|first=Stefan|title=Quantum approximation I. Embeddings of finite-dimensional Lp spaces|journal=Journal of Complexity|language=en|volume=20|issue=1|pages=5–26|arxiv=quant-ph/0305030|doi=10.1016/j.jco.2003.08.002|year=2004|s2cid=6044488}}<br>
{{Cite journal|last=Heinrich|first=Stefan|title=Quantum approximation II. Sobolev embeddings|journal=Journal of Complexity|language=en|volume=20|issue=1|pages=27–45|arxiv=quant-ph/0305031|doi=10.1016/j.jco.2003.08.003|year=2004|s2cid=6061625}}</ref> and high-dimensional integration.<ref>{{Cite journal|last=Heinrich|first=Stefan|title=Quantum Summation with an Application to Integration|journal=Journal of Complexity|language=en|volume=18|issue=1|pages=1–50|arxiv=quant-ph/0105116|doi=10.1006/jcom.2001.0629|year=2002|s2cid=14365504}}<br/>{{Cite journal|last=Heinrich|first=Stefan|date=2003-02-01|title=Quantum integration in Sobolev classes|journal=Journal of Complexity|volume=19|issue=1|pages=19–42|arxiv=quant-ph/0112153|doi=10.1016/S0885-064X(02)00008-0|s2cid=5471897}}<br/>{{Cite journal|last=Novak|first=Erich|title=Quantum Complexity of Integration|journal=Journal of Complexity|language=en|volume=17|issue=1|pages=2–16|arxiv=quant-ph/0008124|doi=10.1006/jcom.2000.0566|year=2001|s2cid=2271590}}</ref>, [[Quantum Cryptography]]
<ref>{{Cite journal|last=Mu|first=Yi|title=Shared cryptographic bits via quantized quadrature phase amplitudes of light|journal=Journal of Optics Communication|language=en|volume=123|pages=334–352|doi=10.1016/0030-4018(95)00688-5|year=1996}}<br/></ref>
== See also ==
| |||